Question

tìm giá trị nhỏ nhất giá trị lớn nhất

a) (2x+5)^2 +(3+x)^2-8

b) (x-4)^2 +x+3

c) (15x-1)+(x-9)^2-27

d) (2-3x).(x+5)-6

e) 4x^2 -3x +2015

Answer 1

a: \(=4x^2+20x+25+x^2+6x+9-8\)

\(=5x^2+26x+26\)

\(=5\left(x^2+\dfrac{26}{5}x+\dfrac{26}{5}\right)\)

\(=5\left(x^2+2\cdot x\cdot\dfrac{13}{5}+\dfrac{169}{25}-\dfrac{39}{25}\right)\)

\(=5\left(x+\dfrac{13}{5}\right)^2-\dfrac{39}{5}>=-\dfrac{39}{5}\)

Dấu '=' xảy ra khi x=-13/5

b: \(=x^2-8x+16+x+3\)

\(=x^2-7x+19\)

\(=x^2-7x+\dfrac{49}{4}+\dfrac{27}{4}=\left(x-\dfrac{7}{2}\right)^2+\dfrac{27}{4}>=\dfrac{27}{4}\)

Dấu '=' xảy ra khi x=7/2

c: \(C=15x-1+x^2-18x+81-27\)

\(=x^2-3x+53\)

\(=x^2-3x+\dfrac{9}{4}+\dfrac{203}{4}=\left(x-\dfrac{3}{2}\right)^2+\dfrac{203}{4}>=\dfrac{203}{4}\)

Dấu '=' xảy ra khi x=3/2